CN106053074B - Rolling bearing sound signal fault feature extraction method based on STFT and rotational inertia entropy - Google Patents
Rolling bearing sound signal fault feature extraction method based on STFT and rotational inertia entropy Download PDFInfo
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- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M13/00—Testing of machine parts
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Abstract
The invention discloses a rolling bearing sound signal fault feature extraction method based on STFT and rotational inertia entropy. The common rolling bearing fault feature extraction method is based on rolling bearing vibration signals, however, requirements for a sensor for collecting rolling bearing vibration data are very high, equipment cost is increased, and a smart phone is used as an important component of daily life, and the rolling bearing operation sound signals can be collected through the recording function of the smart phone. The invention provides a rolling bearing fault feature extraction method based on sound signal short-time Fourier transform (STFT) and rotational inertia entropy. Test result analysis shows that the fault characteristics obtained by the method have excellent classification characteristics and can well support fault diagnosis work of the rolling bearing.
Description
Technical Field
The invention relates to the technical field of rolling bearing tests, in particular to a rolling bearing sound signal fault feature extraction method based on STFT and rotational inertia entropy.
Background
Rolling bearings are one of the widely used standards on various mechanical equipment, and rolling bearing failure is one of the leading causes of machine failure. Statistically, about 30% of the rotary machine failures are related to the rolling bearing failures, so that it is very necessary to diagnose the rolling bearing failures.
One of the key technologies of fault diagnosis is feature extraction, and a good fault feature extraction method is very important for improving the precision of fault diagnosis. The traditional fault diagnosis of the rolling bearing generally performs characteristic extraction aiming at a vibration signal of the rolling bearing, and in various engineering fields, experienced maintenance personnel can judge whether a machine normally operates according to the sound characteristic of the machine during working, for example, in the routine maintenance of a railway system, a worker uses an iron hammer to knock a wheel of a locomotive, and can judge whether cracks exist in the wheel according to the knocking sound. The underlying physical principle is that damage to parts changes their characteristic frequency and thus the pitch of the sound. The related vibration in the operation process of the rolling bearing also causes air compression to generate sound, wherein the sound contains the fault information of the rolling bearing, so that the fault information of the rolling bearing can be obtained by performing feature extraction on the sound signal.
The speech signal is a typical non-stationary signal, and the non-stationary signal is generated by the physical motion process of the sounding body, which is slow compared with the speed of sound wave vibration, and can be assumed to be stationary in a short time of 10-30 ms. Fourier analysis is a powerful means of analyzing the steady-state characteristics of linear systems and stationary signals, while short-time fourier analysis, also called time-dependent fourier transform, is a method of processing non-stationary signals using steady-state analysis methods under the assumption of short-time stationarity. A spectrogram is a time-intensity representation of the short-time spectrum of a speech signal. The speech signal is first divided into several overlapping segments (frames), each segment is windowed, and then fast fourier transformed to obtain a short-time spectrum estimate, i.e. a spectrogram, of the signal. The information entropy can be used for describing the average uncertainty degree of a probability system, the difference of different fault signals in time-frequency distribution is represented as the difference of different time-frequency segment energy distributions on a time-frequency plane, the time-frequency entropy can quantify the difference, and the difference is inspired by the information entropy and the time-frequency entropy, and the different time-frequency segments (namely energy blocks) on the time-frequency plane are different in energy distribution, so that the rotary inertia entropy is defined as the rotary inertia of each energy block to a time axis, a frequency axis and an original point, and the rotary inertia entropy contains the energy difference and the position difference of the time-frequency distribution of voice signals, and can be used as the characteristic of the voice signals to perform subsequent fault diagnosis.
The above description is feasible for feature extraction based on the rolling bearing operation sound data. With the rapid development of electronic information technology, the smart phone has become a life tool which can not be separated, however, the smart phone can be used professionally besides being used as a life tool. Compared with the traditional vibration sensor for collecting data, the intelligent mobile phone has many advantages in collecting fault sound data: firstly, flexibility is realized, data acquisition can be carried out on the running state of the equipment at any time and any place, a sensor does not need to be preinstalled on mechanical equipment in advance, and the installation position of the sensor does not need to be analyzed; secondly, the system is economical, the traditional high-precision sensor is few, thousands of yuan, high and tens of thousands of yuan, the price is high, the intelligent mobile phone with the recording function is only needed to help people to acquire professional data information, specialized use of daily life tools is realized, and the system is convenient, quick, simple and effective; the intelligent mobile phone is suitable for collecting sound information under various working conditions, and the application range is relatively wide.
The smart phone becomes an important part of daily life, and although the recording function of the smart phone is common, the smart phone is rarely used as a data acquisition sensor of fault information in fault diagnosis of equipment.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the traditional vibration signal-based rolling bearing fault diagnosis is high in equipment cost, and the sampling cost is greatly reduced by adopting the smart phone for recording; in addition, the invention defines a new entropy-rotational inertia entropy to express the complexity of time-frequency distribution, so that the obtained fault characteristics have excellent classification characteristics.
The technical scheme adopted by the invention is as follows: a rolling bearing sound signal fault feature extraction method based on STFT and rotational inertia entropy comprises the following steps:
the first step is as follows: obtaining data
Recording sound signals in the bearing operation process according to requirements by using a smart phone, and carrying out certain editing processing;
the second step is that: short-time Fourier analysis (STFT) of speech signals
Reading the preprocessed sound signals by a program, and acquiring a spectrogram and a spectrogram matrix of Matlab by Matlab through a spectral function;
the third step: computing entropy of moment of inertia
Calculating the rotational inertia entropy of the time-frequency distribution of the fault signal, and calculating three rotational inertia entropies(s) of the time-frequency distribution of the fault signal according to the spectrum matrix obtained by STFT calculationt(q),sf(q),so(q))；
The fourth step: feature point representation
And drawing the extracted characteristic values of the rolling bearing in different fault modes in a three-dimensional graph, and analyzing the effectiveness of the method.
Furthermore, the first step is specifically as follows: and a recording function of the smart phone is adopted, the mobile phone is placed beside a bearing of the test bed to acquire voice information of the test bed in operation, and editing processing is carried out.
Furthermore, the second step is specifically as follows: and reading the bearing voice information obtained by sound recording sampling into MATLAB, then carrying out short-time Fourier transform (STFT) on the voice signal, and obtaining a spectrogram of the voice signal by using a spectral function.
Further, the third step is specifically: the patent defines a new entropy calculation method, namely, a rotational inertia entropy, wherein the rotational inertia entropy quantifies the complexity of the time-frequency distribution of fault signals and three rotational inertia entropies(s) of two-dimensional time-frequency distribution of the fault signals by considering the position information of a time-frequency blockt(q),sf(q),so(q)) is specifically defined as follows:
equally dividing the time-frequency plane into N time-frequency blocks with equal area, wherein the energy in each block is EiThe inertia moments of the time-frequency block energy to the time axis t, the frequency axis f and the origin o are respectively as follows:
wherein E isiRepresenting the energy within each block, dtiEnergy of expressionDistance of gauge block to time axis, dfiRepresenting the distance of the energy block to the frequency axis, doiRepresents the distance of the energy block from the origin, JtiRepresenting the moment of inertia of the energy block with respect to the time axis, JfiRepresenting the moment of inertia of the energy mass about the frequency axis, JoiRepresenting the moment of inertia of the energy mass to the origin;
the moment of inertia of the whole time-frequency plane to the time axis t, the frequency axis f and the origin o is respectively as follows:
and normalizing the rotational inertia of the energy of each time frequency block to obtain:
thus, there are:
entropy s of time-frequency distribution of fault signals to moment inertia of time axist(q) entropy of moment of inertia s for frequency axist(q) and entropy of moment of inertia s to origin Oo(q) is defined as follows:
in the formula, qti，qfiAnd q isoiThe ratio of the energy of the ith time frequency block to the rotational inertia of each coordinate axis or origin to the rotational inertia of the corresponding coordinate axis or origin is respectively;
entropy of moment of inertia s for time axist(q) characterizing the complexity of time-frequency distribution to frequency f, namely measuring the distribution condition of fault signal energy in different frequency bands; entropy of moment of inertia s for frequency axisf(q) characterizing the time-frequency distribution versus time complexity, i.e., a time-varying characteristic measure of the fault signal energy distribution; to the originEntropy of moment of inertia s of Oo(q) characterizing the overall complexity of the time-frequency distribution.
Further, the fourth step is specifically: and drawing the rotational inertia entropy calculated after the STFT transformation into a three-dimensional scatter diagram.
Compared with the prior art, the invention has the advantages that:
(1) according to the invention, the sound information of the rolling bearing is collected through the smart phone, so that the hardware cost is greatly reduced compared with the traditional rolling bearing characteristic extraction method based on vibration;
(2) according to the method, the fault voice signals are converted through the STFT, the spectrogram is generated, the fault characteristics are expressed through the defined rotational inertia entropy, and tests prove that the fault characteristics obtained by the method have excellent classification characteristics and can well support the fault diagnosis work of the rolling bearing.
Drawings
FIG. 1 is a flow chart of rolling bearing fault feature extraction based on STFT and rotational inertia entropy;
FIG. 2 is a signal framing;
FIG. 3 is a spectrogram generating process;
FIG. 4 is a time-frequency entropy diagram;
FIG. 5 is a schematic diagram of rotational inertia entropy;
FIG. 6 is a schematic view of a cylindrical roller bearing test stand;
FIG. 7 is a schematic view showing an acoustic signal of a rolling bearing in a normal state;
FIG. 8 is a schematic view of an acoustic signal of a rolling bearing in the event of a failure of the inner ring;
FIG. 9 is a schematic diagram of an acoustic signal of a rolling bearing when a rolling element fails;
FIG. 10 is a schematic diagram showing an acoustic signal of a rolling bearing when an outer ring fails;
FIG. 11 is a spectrogram of the sound signal when the rolling bearing is normal;
FIG. 12 is a spectrogram of an acoustic signal when an inner ring of a rolling bearing has a fault;
FIG. 13 is a spectrogram of an acoustic signal when a rolling element of a rolling bearing is in failure;
FIG. 14 is a spectrogram of sound signals when the outer ring of the rolling bearing has a fault;
fig. 15 is a three-dimensional scatter diagram of the rotational inertia entropy when the rolling bearing is normal, the inner ring is failed, the rolling element is failed, and the outer ring is failed.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
As shown in fig. 1, a rolling bearing acoustic signal fault feature extraction method based on STFT and rotational inertia entropy mainly includes the following steps:
the first step is as follows: obtaining data
And recording sound signals in the bearing running process by using a smart phone according to requirements, and performing certain editing processing.
The second step is that: short-time Fourier analysis (STFT) of speech signals
Reading the preprocessed sound signals by the program, and acquiring a spectrogram and a spectrogram matrix of Matlab by Matlab through a spectral function.
The third step: computing entropy of moment of inertia
And calculating the rotational inertia entropy of the time-frequency distribution of the fault signals. Calculating three rotational inertia entropies(s) of fault signal time-frequency distribution according to the spectrum matrix obtained by STFT calculationt(q),sf(q),so(q))。
The fourth step: feature point representation
And drawing the extracted characteristic values of the rolling bearing in different fault modes in a three-dimensional graph, and analyzing the effectiveness of the method.
The specific embodiment of the invention comprises:
1. speech signal pre-processing
1.1 short-time Fourier transform (STFT) acquisition spectrogram
As a whole, the parameters representing the sound signals are all changed in real time, but are relatively stable within a short time (20-30 ms), so that the sound signals can be regarded as a quasi-steady-state process. The purpose of windowing is to divide the sound signal into short time segments. The audio signal is windowed and framed, the frame length is denoted as N (in ms), the number of frames per second is about 30 frames, and the method of overlapping and segmenting is generally adopted. As shown in fig. 2.
The following are rectangular window and Hamming window (Hamming) functions, the expressions of which are shown in formula (1) and formula (2), and N is the frame length.
Rectangular window:
hanning Window:
the sound signal windowing consists in reducing the slope of both ends. The side lobes of the rectangular window are too high to be satisfactory.
The short-time fourier transform (STFT) of the signal s (t) is defined as follows:
where w (t) is some window function.
The discrete-time STFT expression at any time n is as follows:
the discrete STFT may be obtained by frequency sampling:
S(n,k)＝S(t,f)|f＝k/N,t＝nT (5)
where N is the total number of data points in the window function, which is also the frequency sampling factor. Carrying formula (5) into formula (4) yields a discrete STFT:
where k is greater than or equal to 0 and less than or equal to (N-1), then | x (N, k) | is the estimate of the x (N) short-time amplitude spectrum, and the spectral energy density function (or power spectrum function) p (N, k) at time m is:
P(n,k)＝|x(n,k)|2＝[x(n,k)x(conj(x(n,k)))] (7)
then P (n, k) is a two-dimensional non-negative real-valued function and it is readily proven to be a fourier transform of the short-time autocorrelation function of the signal x (n). The time n is used as an abscissa, k is used as an ordinate, and the value of P (n, k) is expressed as a pseudo color image, i.e., a spectrogram.
The Spectrogram algorithm is an analytical algorithm that produces a two-dimensional image-wise output of a single-bit speech signal (while a matrix of values is also available). The spectrogram takes time n as an abscissa and frequency f as an ordinate, and the value of the energy density spectrum function is expressed as a two-dimensional pseudo-color image. The time-frequency diagram reflecting the dynamic spectrum characteristics of the voice signal has important practical value in voice analysis, and is also called as visual language.
FIG. 3 is a schematic diagram of a spectrogram generation process; the change condition of some frequency domain analysis parameters (such as formants, pitch periods and the like) along with the voice production process (time) can be obtained from the spectrogram; it is also possible to obtain the variation of energy with the speech production process (time), and the magnitude of the pseudo-color value (or gray value) of each pixel of the image represents the signal energy density at the corresponding time and at the corresponding frequency.
1.2 entropy of moment of inertia
(1) Entropy of information
The mathematical definition of information entropy is: let p (p)1,p2,...,pn) Is the probability distribution of a random event, k is an arbitrary constant, generally taken as 1, and the distribution has an information entropy defined as:
the magnitude of the information entropy can be used to characterize the average degree of uncertainty of the probabilistic system. When the probability of occurrence of an event in a certain probability system is 1 and the probability of occurrence of other events is 0, it is known from equation (9) that the information entropy s of the system is 0, and therefore the system is a deterministic system, and the uncertainty is 0. If the probability distribution of a system is uniform, the probability generated by each event in the system is equal, and the information entropy of the system has the maximum value, namely the uncertainty of the system is the maximum. According to this theory, the most uncertain probability distributions have the largest entropy value, and the information entropy value reflects the degree of non-uniformity of their probability distributions.
(2) Time-frequency entropy
The time-frequency distribution of the signals describes the energy distribution condition of the signals at each frequency in sampling time, the time-frequency distribution of the rolling bearings in different working states is different, and in order to quantitatively describe the difference degree, an information entropy theory is introduced into the time-frequency distribution of fault signals. The difference of different fault signals in time frequency distribution shows that the energy distribution of different time frequency segments on a time frequency plane is different, and the time frequency entropy can quantify the difference and further reflect the running state of the machine. As shown in FIG. 4, the time-frequency plane is equally divided into N time-frequency blocks with equal area, and the energy in each block is Ei(i 1.. N), the energy of the whole time-frequency plane is a, and energy normalization is performed on each block to obtain qi＝EiA (i ═ 1.., N), then there areThe normalization condition for calculating the information entropy is met, the calculation formula of the information entropy is imitated, and the calculation formula of the time-frequency entropy of the signal is defined as follows:
(3) entropy of moment of inertia
The definition of the entropy of the slave information and the time-frequency entropy is carried out under the assumption of random variables, namely, no sequence difference exists among the variables. However, after the information entropy is introduced into the field of fault diagnosis, not only the energy size of each energy block needs to be distinguished, but also the position of the energy block needs to be concerned, and the distribution state of the fault signal is accurately measured by integrating the coordinate and the magnitude information. Conversely, if the positions of the time frequency blocks are not considered, the energy values of the time frequency blocks on the time frequency plane are not changed, and the original sequence is disturbed, the calculated time frequency entropy is not changed, and the sequence difference accurately reflects different fault information, which indicates that the fault characteristics cannot be accurately described only by focusing on the information entropy definition form of the values.
In order to comprehensively depict the magnitude information and the position information of fault signal distribution, the invention considers the position of the current time frequency block in the process of defining the entropy and provides the rotational inertia entropy suitable for the problem of fault diagnosis. As shown in FIG. 5, the time-frequency plane is equally divided into N time-frequency blocks of equal area, and the energy in each block is Ei(i 1.. times.n), the moment of inertia of the energy in the time-frequency block to the time axis t, the frequency axis f and the origin O is:
wherein E isiRepresenting the energy within each block, dtiRepresenting the distance of the energy block from the time axis, dfiRepresenting the distance of the energy block to the frequency axis, doiRepresents the distance of the energy block from the origin, JtiRepresenting the moment of inertia of the energy block with respect to the time axis, JfiRepresenting the moment of inertia of the energy mass about the frequency axis, JoiRepresenting the moment of inertia of the energy mass to the origin;
the moment of inertia of the whole time-frequency plane to two coordinate axes and the origin is respectively as follows:
normalizing the rotational inertia of the energy of each time frequency block to obtain
Thus, there are:
the moment of inertia entropy of fault signal time-frequency distribution to time axis, frequency axis and origin O is respectively defined as follows:
in the formula, qti，qfiAnd q isoiAnd the ratio of the energy moment of inertia of the ith time frequency block to the energy moment of inertia of the whole time frequency distribution is respectively.
Entropy of moment of inertia s for time axist(q) characterizing the complexity of time-frequency distribution to frequency f, namely the distribution condition of fault signal energy in different frequency bands; entropy of moment of inertia s for frequency axisf(q) characterizing the time-frequency distribution versus time complexity, i.e., the time-varying characteristics of the fault signal energy distribution; entropy of moment of inertia s to origin Oo(q) characterizing the overall complexity of the time-frequency distribution. Entropy of moment of inertia(s)t(q),sf(q),so(q)) can comprehensively measure the complexity of the time-frequency distribution of the fault signals, and the dimensionality is lower and is suitable for visual analysis, so that the rolling bearing fault diagnosis method can be used as a fault characteristic vector during rolling bearing fault diagnosis.
2. Case verification
2.1 Rolling bearing Acoustic data preparation
As shown in fig. 6, the rolling bearing test stand is a cylindrical roller bearing. In the test process, the rotating speed is set to 1200r/min, and the corresponding shaft frequency is 20 Hz. The sound data acquisition adopts the recording software in the Samsung note3 mobile phone, and the mobile phone is close to the bearing of the bearing test bed in the acquisition process, and the sampling frequency is 44.1 kHz. The collected data covers 4 fault modes of normal state, outer ring fault, inner ring fault and rolling body fault.
2.2 Rolling bearing fault feature extraction test analysis under sound data condition
The sound data signals of the normal state, the inner ring failure, the rolling element failure, and the outer ring failure are shown in fig. 7 to 10. This patent selects the frame length (window) to be 5120, the slip length (noverlap) to be 1020, the discrete fourier transform length (nfft) to be 1024 (equal to the window length and the sampling frequency), the sampling frequency fs 44100, and uses a Hanning window to generate a spectrogram. The spectrogram is shown in FIGS. 11-14. After the spectrogram is generated, the rotational inertia entropy of the spectrogram with respect to the time axis, the frequency axis, and the origin is calculated and then the calculated rotational inertia entropy is plotted in a three-dimensional scattergram, as shown in fig. 15.
Claims (3)
1. A rolling bearing sound signal fault feature extraction method based on STFT and rotational inertia entropy is characterized by comprising the following steps: recording by adopting a smart phone; defining an entropy-rotational inertia entropy to represent the complexity of time-frequency distribution, comprising the following steps:
the first step is as follows: obtaining data
Recording sound signals in the bearing operation process according to requirements by using a smart phone, and carrying out certain editing processing;
the second step is that: short-time Fourier analysis (STFT) of voice signal
Reading the preprocessed sound signals by a program, and acquiring a spectrogram and a spectrogram matrix of Matlab by Matlab through a spectral function;
the third step: computing entropy of moment of inertia
Calculating the rotational inertia entropy of the time-frequency distribution of the fault signal, and calculating three rotational inertia entropies(s) of the time-frequency distribution of the fault signal according to the spectrum matrix obtained by STFT calculationt(q),sf(q),so(q))；
The third step is specifically: defining a calculation method of rotational inertia entropy, wherein the rotational inertia entropy quantifies the time-frequency distribution complexity of a fault signal and three rotational inertia entropies(s) of two-dimensional time-frequency distribution of the fault signal by considering the position information of a time-frequency blockt(q),sf(q),so(q)) is specifically defined as follows:
equally dividing the time-frequency plane into N time-frequency blocks with equal area, wherein the energy in each block is EiThe inertia moments of the time-frequency block energy to the time axis t, the frequency axis f and the origin o are respectively as follows:
wherein E isiRepresenting the energy within each block, dtiRepresenting the distance of the energy block from the time axis, dfiRepresenting the distance of the energy block to the frequency axis, doiTo representDistance of energy block to origin, JtiRepresenting the moment of inertia of the energy block with respect to the time axis, JfiRepresenting the moment of inertia of the energy mass about the frequency axis, JoiRepresenting the moment of inertia of the energy mass to the origin;
the moment of inertia of the whole time-frequency plane to the time axis t, the frequency axis f and the origin o is respectively as follows:
and normalizing the rotational inertia of the energy of each time frequency block to obtain:
thus, there are:
entropy s of time-frequency distribution of fault signals to moment inertia of time axist(q) entropy of moment of inertia s for frequency axist(q) and entropy of moment of inertia s to origin Oo(q) is defined as follows:
in the formula, qti，qfiAnd q isoiThe ratio of the energy of the ith time frequency block to the rotational inertia of each coordinate axis or origin to the rotational inertia of the corresponding coordinate axis or origin is respectively;
entropy of moment of inertia s for time axist(q) characterizing the complexity of time-frequency distribution to frequency f, namely measuring the distribution condition of fault signal energy in different frequency bands; entropy of moment of inertia s for frequency axisf(q) characterizing the time-frequency distribution versus time complexity, i.e., a time-varying characteristic measure of the fault signal energy distribution; entropy of moment of inertia s to origin Oo(q) comprehensive complexity of characterizing time-frequency distributions；
The fourth step: feature point representation
Drawing the extracted characteristic values of the rolling bearing in different fault modes in a three-dimensional graph, and analyzing the effectiveness of the method;
the fourth step is specifically as follows: drawing the rotational inertia entropy calculated after the STFT transformation in a three-dimensional scatter diagram;
the method transforms a fault voice signal through STFT and generates a spectrogram, and expresses fault characteristics through defined rotational inertia entropy.
2. The rolling bearing sound signal fault feature extraction method based on the STFT and the rotational inertia entropy as claimed in claim 1, wherein: the first step is specifically: and a recording function of the smart phone is adopted, the mobile phone is placed beside a bearing of the test bed to acquire voice information of the test bed in operation, and editing processing is carried out.
3. The rolling bearing sound signal fault feature extraction method based on the STFT and the rotational inertia entropy as claimed in claim 1, wherein: the second step is specifically as follows: and reading the bearing voice information obtained by sound recording sampling into MATLAB, then carrying out short-time Fourier transform (STFT) on the voice signal, and obtaining a spectrogram of the voice signal by using a spectral function.
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| CN109783767B (en) * | 2018-12-21 | 2023-03-31 | 电子科技大学 | Self-adaptive selection method for short-time Fourier transform window length |
| CN111122163A (en) * | 2019-09-19 | 2020-05-08 | 人本集团有限公司 | Bearing fault detection system |
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